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Dana Scott

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Theory & Models of Lambda Calculus: Typed and Untyped (Part 6)LambdaConf 20182018-06-03
Claims a concrete model: using the powerset of the integers with enumeration operators to model application, abstraction and computability, then adds a…
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Theory & Models of Lambda Calculus: Typed and Untyped (Part 5)LambdaConf 20182018-06-03
Model uses the powerset of N with enumeration operators to model application and abstraction; closure operators correspond to subspaces and fixed points equal…
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Theory & Models of Lambda Calculus: Typed and Untyped (Part 3)LambdaConf 20182018-06-03
Presents a concrete model: represent data as subsets of N and functions as enumeration operators on P(N) so application becomes a lookup-table operation on…
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Theory & Models of Lambda Calculus: Typed and Untyped (Part 3)LambdaConf 20182018-06-03
Claims a concrete model of lambda calculus built on the powerset of the integers, using enumeration operators as the actual implementation of application and…
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Theory & Models of Lambda Calculus: Typed and Untyped (Part 2)LambdaConf 20182018-06-03
Claims a concrete semantic model: use the powerset of the integers with enumeration operators to interpret application and abstraction, and show that Church…
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Theory & Models of Lambda Calculus: Typed and Untyped (Part 1)LambdaConf 20182018-06-03
Shows a concrete model: application and abstraction realized by enumeration operators on P(N) with a topology, not handwavy category talk. Carries out…
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Theory and Models of Lambda Calculus Untyped and Typed - Part 1 of 5LambdaConf 20172017-05-25
History ties Church and Curry to later work while a hands‑on session uses Mathematica rewrite rules to test combinators, demonstrating concrete reductions like…
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Theory and Models of Lambda Calculus Untyped and Typed - Part 2 of 5LambdaConf 20172017-05-25
Concrete claims and artifacts: an algorithm that converts lambda abstractions into S and K combinators, worked examples and a Mathematica notebook with tests…
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Theory and Models of Lambda Calculus Untyped and Typed - Part 3 of 5LambdaConf 20172017-05-25
Part 3 lays out concrete constructions and results: lambda abstraction is realized as the largest lookup table that reproduces a continuous operator; pure…
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Theory and Models of Lambda Calculus Untyped and Typed - Part 4 of 5LambdaConf 20172017-05-25
Constructs models inside P(N) using enumeration operators and least fixed points to show that closure operators form a cartesian closed category and that…
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Theory and Models of Lambda Calculus Untyped and Typed - Part 5 of 5LambdaConf 20172017-05-25
Shows how untyped lambda over PERs and the power set of N with Scott topology produce models of dependent and polymorphic type theory, giving a local cartesian…
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